New European rules come into force today which mean some women are set for a shock when their next car insurance quote lands on the doormat.

The new gender-neutral rules stem from a European Court of Justice ruling last year which means insurers are no longer able to consider a customer's gender when calculating how much they pay for their car or life insurance, or what their retirement income should be.

Women have benefited from smaller car insurance premiums due to their lower accident rates, and predictions as to how they will be affected have varied widely.

Some analysts believe younger women could see their premiums almost double, while others forecast that the increases could be more gentle than expected, provided insurers can piece together enough information about someone as a driver.

Young women are likely to bear the brunt of the increases, due to the higher accident rates of young men, which experts warn could force many younger female drivers off the road. Meanwhile, some men could see a small reduction in their premiums.

While the full impact of the changes is yet to be seen, price comparison website Gocompare has already seen women's premiums jump in recent days.

The figures show that the average best price for female car insurance has gone up from £748 on 1 November 2012 to £932 on 19 December 2012.

However, male premiums are virtually unchanged for the same period.

The average best price for 17- and 18-year-old females has risen 32 per cent from £1,910 at the start of November this year to £2,523.

Male 17- and 18-year-old premiums have decreased by 10 per cent over the same period from £3,855 to £3,460, Gocompare said.

The site, which says it has monitored more than 10 million car insurance quotes since January last year, said this is the biggest shift it has seen in premiums so far.

Another comparison website, MoneySupermarket, said that although it is yet to see any great spike in prices, this could change quickly as insurers jostle for position in the fast-moving market.

The website's insurance expert, Kevin Pratt, said: "There may be a period of a few days or weeks when the market adjusts. There are over 100 companies trying to get business and they will inevitably monitor what the others are doing."

Mr Pratt said he hopes insurers will place greater emphasis on other factors to make sure drivers can still get a reasonable price, such as their job, type of car, driving record, any security measures on the car and age.

There is no reason why someone cannot continue to be deserving of the premium they are paying at the moment, provided the insurer can find out sufficient information about them, he said.

Michael Ossei, a personal finance expert at uSwitch.com, predicted that women aged between 17 and 25 could see premiums "almost double".

The website said that more than a third of the women it has surveyed would have to cut back their living expenses to cope with higher premiums and one in 10 (11%) may end up selling their car.

There are also signs that it is getting harder for young people to get a broader choice of car insurance quotes.

Gocompare found that 17-year-olds looking for insurance get an average of 32 quotes, three fewer than at the start of November.

Insurer Aviva recently found that a third of parents who help with their children's car insurance believe higher premiums when the new rules come in will force them to give up these payments.

Ian Crowder, spokesman for AA Insurance which monitors quotes across the industry, said: "The youngest drivers will be most affected. That's because young men are more than twice as likely to be killed or seriously injured in a car crash than their female peers.

"Young women aged 17-22 typically pay up to 40% less for their cover than young men; well, until now at any rate. In middle age, there is little difference in premiums between the genders."

Premiums are dropping by up to 10% for men aged 25 and below and are increasing by up to 30% for the youngest women drivers, Mr Crowder said.

Despite the concerns this will raise, experts advise drivers not to suddenly ditch their policy to try to lock into a better deal. They may then be hit with a cancellation fee which could eat into any savings made and jeopardise their no-claims bonus, as successive years of insurance need to be built up.

The Association of British Insurers has placed guidance about the changes on its website. It urges customers not to focus on price alone but to shop around for the most suitable deal.

Drivers can push their costs down by paying their car insurance in one lump sum rather than instalments, having a "black box" installed in their car which rewards careful driving with lower premiums and having extra security measures fitted, it suggests.